Surface Area and Volume PowerPoint. ppt
- 1. Surface Area and Surface Area and Volume Volume
- 2. Surface Area of Prisms Surface Area of Prisms Surface Area Surface Area = The total area of the surface of a = The total area of the surface of a three-dimensional object three-dimensional object (Or think of it as the amount of paper you’ll need to (Or think of it as the amount of paper you’ll need to wrap the shape.) wrap the shape.) Prism Prism = = A solid object that has two identical ends and A solid object that has two identical ends and all flat sides. all flat sides. We will start with 2 prisms – a We will start with 2 prisms – a rectangular prism rectangular prism and and a a triangular prism. triangular prism.
- 4. Surface Area (SA) of a Rectangular Surface Area (SA) of a Rectangular Prism Prism Like dice, there are six sides (or 3 pairs of sides)
- 5. Prism net - unfolded Prism net - unfolded
- 6. • Add the area of all 6 sides to find the Surface Add the area of all 6 sides to find the Surface Area. Area. 10 - length 5 - width 6 - height
- 7. SA = 2lw + 2lh + 2wh SA = 2lw + 2lh + 2wh 10 - length 5 - width 6 - height SA = 2lw + 2lh + 2wh SA = 2 (10 x 5) + 2 (10 x 6) + 2 (5 x 6) = 2 (50) + 2(60) + 2(30) = 100 + 120 + 60 = 280 units squared
- 8. Practice Practice 10 ft 12 ft 22 ft SA = 2lw + 2lh + 2wh = 2(22 x 10) + 2(22 x 12) + 2(10 x 12) = 2(220) + 2(264) + 2(120) = 440 + 528 + 240 = 1208 ft squared
- 9. Surface Area of a Triangular Prism Surface Area of a Triangular Prism •2 bases (triangular) •3 sides (rectangular)
- 10. Unfolded net of a triangular prism Unfolded net of a triangular prism
- 11. 2(area of triangle) + Area of 2(area of triangle) + Area of rectangles rectangles 15ft Area Triangles = ½ (b x h) = ½ (12 x 15) = ½ (180) = 90 Area Rect. 1 = b x h = 12 x 25 = 300 Area Rect. 2 = 25 x 20 = 500 SA = 90 + 90 + 300 + 500 + 500 SA = 1480 ft squared
- 12. Practice Practice 10 cm 8 cm 9 cm 7 cm Triangles = ½ (b x h) = ½ (8 x 7) = ½ (56) = 28 cm Rectangle 1 = 10 x 8 = 80 cm Rectangle 2 = 9 x 10 = 90 cm Add them all up SA = 28 + 28 + 80 + 90 + 90 SA = 316 cm squared
- 13. Surface Area of a Cylinder Surface Area of a Cylinder
- 14. Review Review •Surface area is like the amount of paper you’ll need to wrap the shape. •You have to “take apart” the shape and figure the area of the parts. •Then add them together for the Surface Area (SA)
- 15. Parts of a cylinder Parts of a cylinder A cylinder has 2 main parts. A rectangle and A circle – well, 2 circles really. Put together they make a cylinder.
- 16. The Soup Can The Soup Can Think of the Cylinder as a soup can. Think of the Cylinder as a soup can. You have the top and bottom lid You have the top and bottom lid ( (circles circles) and you have the label (a ) and you have the label (a rectangle rectangle – wrapped around the – wrapped around the can). can). The lids and the label are related. The lids and the label are related. The circumference of the lid is the The circumference of the lid is the same as the length of the label. same as the length of the label.
- 17. Area of the Circles Area of the Circles Formula for Area of Circle Formula for Area of Circle A= A= r r2 2 = 3.14 x 3 = 3.14 x 32 2 = 3.14 x 9 = 3.14 x 9 = 28.26 = 28.26 But there are 2 of them so But there are 2 of them so 28.26 x 2 = 56.52 units squared 28.26 x 2 = 56.52 units squared
- 18. The Rectangle The Rectangle This has 2 steps. To find the area we need base and height. Height is given (6) but the base is not as easy. Notice that the base is the same as the distance around the circle (or the Circumference).
- 19. Find Circumference Find Circumference Formula is Formula is C = C = x d x d = 3.14 x 6 (radius doubled) = 3.14 x 6 (radius doubled) = 18.84 = 18.84 Now use that as your base. Now use that as your base. A = b x h A = b x h = 18.84 x 6 (the height given) = 18.84 x 6 (the height given) = 113.04 units squared = 113.04 units squared
- 20. Add them together Add them together Now add the area of the circles and Now add the area of the circles and the area of the rectangle the area of the rectangle together. together. 56.52 + 113.04 = 169.56 units 56.52 + 113.04 = 169.56 units squared squared The total Surface Area! The total Surface Area!
- 21. Formula Formula SA = ( SA = ( d x h) + 2 ( d x h) + 2 ( r r2 2 ) ) Label Label Lids (2) Lids (2) Area of Rectangle Area of Circles Area of Rectangle Area of Circles
- 22. Practice Practice Be sure you know the difference between a radius and a diameter! Be sure you know the difference between a radius and a diameter! SA = ( SA = ( d x h) + 2 ( d x h) + 2 ( r r2 2 ) ) = (3.14 x 22 x 14) + 2 (3.14 x 11 = (3.14 x 22 x 14) + 2 (3.14 x 112 2 ) ) = (367.12) + 2 (3.14 x 121) = (367.12) + 2 (3.14 x 121) = (367.12) + 2 (379.94) = (367.12) + 2 (379.94) = (367.12) + (759.88) = (367.12) + (759.88) = 1127 cm = 1127 cm2 2
- 23. More Practice! More Practice! SA SA = ( = ( d x h) + 2 ( d x h) + 2 ( r r2 2 ) ) = (3.14 x 11 x 7) + 2 ( 3.14 x 5.5 = (3.14 x 11 x 7) + 2 ( 3.14 x 5.52 2 ) ) = (241.78) + 2 (3.14 x 30.25) = (241.78) + 2 (3.14 x 30.25) = (241.78) + 2 (3.14 x 94.99) = (241.78) + 2 (3.14 x 94.99) = (241.78) + 2 (298.27) = (241.78) + 2 (298.27) = (241.78) + (596.54) = (241.78) + (596.54) = = 838.32 cm 838.32 cm2 2 11 cm 7 cm
- 24. Surface Area of a Surface Area of a Pyramid Pyramid
- 25. Pyramid Nets Pyramid Nets A pyramid has 2 A pyramid has 2 shapes: shapes: One (1) square One (1) square & & Four (4) triangles Four (4) triangles
- 26. Since you know how to find the Since you know how to find the areas of those shapes and add areas of those shapes and add them. them. Or… Or…
- 27. you can use a formula… you can use a formula… SA = ½ lp + B Where l is the Slant Height and p is the perimeter and B is the area of the Base
- 28. SA = ½ lp + B 6 7 8 5 Perimeter = (2 x 7) + (2 x 6) = 26 Slant height l = 8 ; SA = ½ lp + B = ½ (8 x 26) + (7 x 6) *area of the base* = ½ (208) + (42) = 104 + 42 = 146 units 2
- 29. Practice Practice 6 6 18 10 SA = ½ lp + B = ½ (18 x 24) + (6 x 6) = ½ (432) + (36) = 216 + 36 = 252 units2 Slant height = 18 Perimeter = 6x4 = 24 What is the extra information in the diagram?
- 31. Volume of Prisms and Cylinders Volume of Prisms and Cylinders
- 32. Volume Volume • The number of cubic units needed to fill the shape. Find the volume of this prism by counting how many cubes tall, long, and wide the prism is and then multiplying. • There are 24 cubes in the prism, so the volume is 24 cubic units. 2 x 3 x 4 = 24 2 – height 3 – width 4 – length
- 33. Formula for Prisms Formula for Prisms VOLUME OF A PRISM VOLUME OF A PRISM The volume The volume V V of a prism is the of a prism is the area of its base area of its base B B times its height times its height h h. . V V = = Bh Bh Note – the capital letter stands for the AREA of the Note – the capital letter stands for the AREA of the BASE not the linear measurement. BASE not the linear measurement.
- 34. Try It Try It 4 ft - width 3 ft - height 8 ft - length V = Bh Find area of the base = (8 x 4) x 3 = (32) x 3 Multiply it by the height = 96 ft3
- 35. Practice Practice 12 cm 10 cm 22 cm V = Bh = (22 x 10) x 12 = (220) x 12 = 2640 cm3
- 36. Cylinders Cylinders VOLUME OF A CYLINDER VOLUME OF A CYLINDER The volume The volume V V of a cylinder is the area of a cylinder is the area of its base, of its base, r r2 2 , times its height , times its height h h. . V V = = r r2 2 h h Notice that Notice that r r2 2 is the formula for area is the formula for area of a circle. of a circle.
- 37. Try It Try It V = r2 h The radius of the cylinder is 5 m, and the height is 4.2 m V = 3.14 · 52 · 4.2 V = 329.7 Substitute the values you know.
- 38. Practice Practice 7 cm - height 13 cm - radius V = r2 h Start with the formula V = 3.14 x 132 x 7 substitute what you know = 3.14 x 169 x 7 Solve using order of Ops. = 3714.62 cm3
- 39. Lesson Quiz Find the volume of each solid to the nearest tenth. Use 3.14 for . 861.8 cm3 4,069.4 m3 312 ft3 3. triangular prism: base area = 24 ft2 , height = 13 ft 1. 2.
- 40. Volume of Pyramids Volume of Pyramids
- 41. Remember that Volume of a Prism is B x h where b is the area of the base. You can see that Volume of a pyramid will be less than that of a prism. How much less? Any guesses?
- 42. Volume of a Pyramid: V = (1/3) Area of the Base x height V = (1/3) Bh Volume of a Pyramid = 1/3 x Volume of a Prism If you said 2/3 less, you win! + + =
- 43. Find the volume of the square pyramid with base edge length 9 cm and height 14 cm. The base is a square with a side length of 9 cm, and the height is 14 cm. V = 1/3 Bh = 1/3 (9 x 9)(14) = 1/3 (81)(14) = 1/3 (1134) = 378 cm3 14 cm
- 44. Practice Practice V = 1/3 Bh = 1/3 (5 x 5) (10) = 1/3 (25)(10) = 1/3 250 = 83.33 units3
- 45. Quiz Quiz Find the volume of each figure. 1. a rectangular pyramid with length 25 cm, width 17 cm, and height 21 cm 2975 cm3 2. a triangular pyramid with base edge length 12 in. a base altitude of 9 in. and height 10 in. 360 in3
- 46. End End